Designing fractional two-level experiments with nested error structures

A common feature of experiments with a random blocking factor and splitplot experiments is their nested error structure. This paper proposes a general strategy to handle fractional two-level experiments with such error structures. The strategy aims to create error strata with sufficient numbers of contrasts to separate active effects from inactive effects. The strategy also details the construction of treatment generators, given the constraints of a predetermined error structure. The key elements of the strategy are illustrated with a chemical experiment that has 16 factors and 32 runs blocked according to working days, and a cheese-making experiment that has 11 factors and 128 runs, divided over milk supplies as whole plots, curds productions as subplots and sets of identically treated cheeses as sub-subplots.